Analytical Redundancy Design for Aeroengine Sensor Fault Diagnostics Based on SROS-ELM

Analytical redundancy technique is of great importance to guarantee the reliability and safety of aircraft engine system. In this paper, a machine learning based aeroengine sensor analytical redundancy technique is developed and verified through hardwarein-the-loop (HIL) simulation. The modified online sequential extreme learning machine, selective updating regularized online sequential extreme learning machine (SROS-ELM), is employed to train the model online and estimate sensor measurements. It selectively updates the output weights of neural networks according to the prediction accuracy and the norm of output weight vector, tackles the problems of singularity and ill-posedness by regularization, and adopts a dual activation function in the hidden nodes combing neural and wavelet theory to enhance prediction capability.The experimental results verify the good generalization performance of SROS-ELM and show that the developed analytical redundancy technique for aeroengine sensor fault diagnosis based on SROS-ELM is effective and feasible.


Introduction
As the control and health management of aircraft engine highly relies on the precise and reliable sensor measurements, sensor is one of the most important components of the aeroengine system.With the increase of control and monitoring variables, the types and number of sensors used in aeroengine are growing [1].However, most sensors work in severe environment of high temperature, high pressure, and strong vibration which is also changing rapidly [2]; thus they are very vulnerable to breakdown.Therefore, some measures should be adopted to ensure the correctness of sensor readings.For this challenge, sensor redundancy technique is a good solution.Generally there are two kinds of sensor redundancy: one is hardware redundancy and the other is analytical redundancy [3].Hardware redundancy adopts more than one sensor to measure the same engine variable, but it is at the price of extra cost, maintenance, additional weight, and more space to furnish sensors.Analytical redundancy constructs redundant estimates of the sensor readings using numerical algorithms to reduce the weight and cost of aeroengine.With the remarkable advantages, the analytical redundancy technique has been widely researched and applied in aeroengine system since it originated.Wallhagen and Arpasi demonstrated the application of sensor analytical redundancy technique for enhancing the reliability of engine control system [4].Corley et al. developed a fault indication and correction (FICA) system and employed it to engine control system for T700, JTDE, and F404, which laid the theoretical basis and set an excellent example for the application of analytical redundancy in engine control system [5,6].
The analytical redundancy design methods fall into three categories: model-based, data-driven, and the hybrid approach.Model-based techniques can be utilized to diagnose new sensor faults with no prior knowledge and experience, but it depends on accurate on-board adaptive engine model whose reliability may decline with the increase of modeling uncertainties and nonlinear complexities [7].On the other side, the data-driven method needs no knowledge about the intricate engine working principle and complicated modeling skills and thus attracts lots of interest and concern.Botros et al. presented an application of optimized radial basis function neural networks based data mining to sensor faults detection on gas-turbine-driven compressor stations [8].Huang employed autoassociative neural networks to detect sensor failures at the absence of models and reconstruct engine control system [9].Joly et al. developed a gas-turbine diagnostics structure using several artificial neural networks for a high bypass ratio military turbofan engine [10].Ogaji et al. also conceived artificial neural networks based sensor faults diagnosis for gas-turbine.The system was trained to detect, isolate, and assess faults [11].However, most of the existed methods are trained offline, which cannot capture and adapt to the dynamic changes of system characteristics.Besides, conventional machine learning algorithms that the analytical redundancy technique is based on have weakness such as learning samples slowly and requiring massive computing resource.
Extreme learning machine (ELM) is a novel and efficient learning algorithm for training single-hidden layer feedforward neural networks (SLFNs) proposed by Huang et al. [12].It has been proven that ELM method has not only classification capability but also universal approximation capability [13,14].In addition, as verified in [14], ELM can learn much faster than traditional SVM, LS-SVM, and neural networks while achieving similar or much better generalization performance.Nevertheless, ELM is an offline learning algorithm.In order to learn data one-by-one or chunk-by-chunk online, Liang et al. proposed a fast and accurate online sequential extreme learning machine (OS-ELM) based on the idea of ELM [15].Different from adjusting learning parameters iteratively like gradient-based neural networks does, it randomly generates input weights and hidden biases and determines the output weights analytical according to the sequentially arriving data.However, there are still limitations such as singularity and ill-posedness problems, potentially inconsistent and unstable performance.To alleviate such weaknesses, this paper proposed a modified online sequential extreme learning machine, selective updating regularized online sequential extreme learning machine (SROS-ELM).And then an aeroengine analytical redundancy technique based on that is developed and verified through HIL simulation.
The rest of this paper is organized as follows.Section 2 gives a brief review of OS-ELM.Section 3 presents SROS-ELM algorithm and evaluates its performance.Section 4 describes the analytical redundancy technique based on SROS-ELM in detail.The verification of the developed technique through hardware-in-the-loop (HIL) simulation is shown in Section 5. Conclusions are drawn in Section 6.

Brief Review of OS-ELM
For  arbitrary distinct samples (x  , t  ), where T ∈   is the target vector.The output function of SLFN with  hidden neurons and activation function () can be represented as where w  = [ 1 ,  2 , . . .,   ] T is the weight vector connecting the input layer and the th hidden neuron,   = [ 1 ,  2 , . . .,   ] T is the weight vector connecting the th hidden neuron and the output layer, and   is the bias of the th hidden neuron.
The  equations can be written in form of matrix where H is named hidden layer output matrix [12].The hidden node parameters w  and   are simply assigned with random values and need not to be tuned.Thus, the output weight vector  is the only parameter that needs to be calculated.The determination of the output weights can be simplified as seeking the least-square solution to the given linear system, which may be expressed as where H † is Moore-Penrose generalized inverse of matrix H, which can be calculated through orthogonal projection as For (5), it is can be solved recursively by [15] where and the initialization procedure can be completed by The OS-ELM algorithm is suitable for SLFNs with additive or RBF hidden nodes.It can deal with sequential learning tasks much faster than other sequential algorithms with good prediction accuracy.However, the analytical determination of the output weights according to formula ( 5) is on the hypothesis that H T H is nonsingular which is not always satisfied.Besides, the ill-posedness or singularity problems have not been paid attention to, which may do great harm to the generalization performance.Furthermore, the output weights are always updated and the debasement in generalization performance because of some new arriving samples has not been considered.The solution for these problems will be investigated in the next section.

SROS-ELM
In this section, the SROS-ELM is proposed on the basis of OS-ELM and its performance is evaluated on some benchmark data sets.

Formula Derivation.
On the basis of ridge regression theory [18], the stability will be improved and better generalization performance can be achieved by introducing a positive value , which is also called the regularization factor, to the diagonal elements of H T H when determining the output weight vector  [19].Thus, formula (5) becomes as follows: In order to train the SLFNs online, now we need to derivate the recursive formula for updating the output weights.
For an initial training subset, Ω = {x  , t  }  0 1 , the initial output weight vector  0 can be estimated by where T , and Supposing that there is a new sample {x  0 +1 , t  0 +1 }, the output weights can be determined by where substituting this into (10), then the output weights become In generalization, for the (+1)th observation, the output weights can be updated by L +1 is a matrix with the size of  × , where  denotes the number of hidden nodes in neural networks.As the number of hidden nodes is usually quite large and the computation of the inverse matrix is resource consuming, the update formula for L −1 +1 can be expressed using Woodbury formula [20] so as to save computing cost: When the new samples arrive one-by-one rather than blockby-block, formula ( 14) can be written in a simple format on the basis of Sherman-Morrison formula [20]: Let P  = L −1  ; then the equations for updating become Further, P +1 h T +1 can be written as Let ; a simple recursive formula for the output weights can be achieved: As investigated by Zhu et al. [21] and Bartlett [22], the prediction accuracy of neural networks is determined by not only the training error but also the norm of output weights.The networks with weights of smaller norm tend to perform superior generalization.Taking account of these two factors, the output weights are updated selectively according to both the prediction error and the norm of output weights: where   = ‖t +1 − t+1 ‖ = ‖t +1 − h +1   ‖ denotes the prediction error of t +1 and  is the threshold for decision.
Based on the theory proposed by [23], the activation functions of the hidden nodes have great impact on the performance of neural networks.As verified in [24], the neural networks taking inverse hyperbolic sine and Morlet wavelet as dual activation function can enhance dealing with nonlinearity and dynamic systems and achieve promising performance.Following that, this paper adopts a dual activation function in the hidden units combing neural and wavelet theory to improve prediction capability: In summary, the procedure of the SROS-ELM goes as follows: (1) Initialization: for the initial training subset, Ω = {x  , t  }  0 1 ,  0 ≥ , (a) randomly set the value of input weights w  and bias   ,  = 1, 2, . . .,  and choose a proper ; (b) calculate hidden layer output matrix (c) estimate the initial output weight vector  0 ,  0 = P 0 H T 0 T 0 , where (d) set  = 0.

Evaluation Test.
As aeroengine analytical redundancy design using machine learning is a regression problem, the proposed SROS-ELM is evaluated on some real-world regression applications which are also used in [15] and the performance is compared with some popular algorithms.A sigmoid function is taken as hidden unit activation function for OS-ELM, while in SROS-ELM dual activations combining inverse hyperbolic sine function and Morlet wavelet are adopted.Since SROS-ELM has the same computational complexity as OS-ELM, there is no need to take the comparison of training and testing time into consideration.The root mean square error (RMSE) which is defined as the deviation measurement between the predicted and the target values is taken as the performance criterion.Table 1 has listed the average results of fifty trials on different benchmark data sets.From Table 1, it is obvious that the proposed SROS-ELM outperforms OS-ELM in generalization performance while the numbers of hidden nodes are the same.Moreover, the SROS-ELM always achieves smaller RMSE than some other popular sequential learning algorithms; thus it is more suitable for aeroengine analytical redundancy design which will be illustrated specifically in the next section.

Aeroengine Analytical Redundancy Design
As the reliability and safety of aircraft engine system can never be emphasized too much and sensor fault diagnostics plays an important role in guaranteeing them, in this section an analytical redundancy technique based on SROS-ELM is developed for sensor fault detection, isolation, and accommodation.Figure 1 illustrates the schematic, which works as follows: firstly the engine control inputs and sensor measurements are pretreated and reorganized for the SROS-ELM based senor measurement estimators, following that the estimators perform the estimations for the corresponding sensor measurements according to the inputs of SROS-ELM, finally the sensor fault detection, isolation, and accommodation are achieved with the fault diagnosis and signal reconstruction strategy.
From Figure 1 it can be seen that six estimators are built and each is separately responsible for the estimation of the fan speed (  ), the core speed ( ℎ ), the pressure after compressor ( 3 ), the temperature after compressor ( 3 ), the pressure after low pressure turbine ( 45 ), and the temperature after low pressure turbine ( 45 ).For every estimator, the inputs are composed of the engine control inputs such as the main fuel flow and the nozzle throat area and the other five sensors' measurements.With the aim to enhance the estimation capability and obtain good accuracy especially during dynamic process, not only the current control inputs and sensor measurements but also the values of some previous steps are adopted as the neural networks' inputs.
The estimator based on RSOS-ELM for each sensor can be expressed as where d  is the estimation of the th sensor, y  is an vector obtained by removing the th sensor value from all the six sensors' measurements y, u = [   8 ] denotes the engine control inputs including the fuel flow   and the nozzle throat area  8 , and  is the embedded dimension.
The fault detection and isolation are realized by comparing the residuals to the fault threshold FC.The residuals are defined as the deviations between the estimated and measured sensor values: where d  represents the estimated value for the th sensor and    denotes the measured value of the th sensor.If    < FC, it can be judged that the th sensor is normal; otherwise the sensor is faulty.Once a sensor is found to break down, the estimated value by the estimator will take place of the incorrect sensor measurement to achieve fault accommodation.Therefore, reliable and accurate sensor signal d  can be provided for engine control and health management.

Verification through HIL Simulation
Hardware-in-the-loop simulation is an efficient way for the verification and validation of safety-critical control system such as aeroengine control system [25].It enables the realtime simulation wherein the actual controller or important components under test couple with the simulated plant in a manner similar to the real-world, which can effectively save the development cost and reduce the risks of accident occurring at test [26].Hence, HIL simulation is widely applied in industry and recommended by Electrical and Electronics Engineers (IEEE), International Atomic Energy Agency (IAEA), and the United States Nuclear Regulatory Commission (US-NRC) [27].Aiming at verifying the developed aeroengine analytical redundancy technique, the HIL simulation platform for engine control system in the laboratory is introduced and then some HIL simulation experiments are performed and analyzed in this section.

HIL Simulation
System.The HIL simulation system for the design and testing of aeroengine control system is mainly composed of model computer, simulator, electronic engine controller (EEC), fuel subsystem, and aeroengine shaft rotating speed simulating subsystem.What is more, it can be used to inject sensor faults to test the sensor fault diagnosis method and the fault-tolerance control ability of EEC.The fuel subsystem is employed to provide a working condition similar to the real-world for the actuators in fuel control loop; thus this HIL simulation is also called wet rig test.As shown in Figure 3, the fuel subsystem mainly consists of fuel tank, booster pump, flowmeter, fuel regulator, pips, and many sensors.Fuel regulator is one of the most important actuators in engine control system.It is a key component in fuel subsystem which needs to be evaluated, so the actual object is utilized in the test system.The rotating speed of rotor in aeroengine is simulated by a motor.In general, the whole HIL simulation system provides a flexible simulated testing environment for the verification and validation of engine control and health management units. of aircraft engine is consistent with that of a second-order inertial element, the value of embedded dimension is chosen to be  = 2.The threshold is selected as FC = 0.015 after trial and error.In order to evaluate the estimation accuracy of SROS-ELM, an assessment criterion which represents the sensor estimation relative deviation is defined as follows:

HIL Simulation
Firstly, sensor faults under steady state are simulated for the six sensors, respectively.With the throttle lever randomly pushed and pulled at the height of  = 0 and the Mach number of Ma = 0, a bias fault with the magnitude of 3% is injected into  45 at time of 53.52 s. Figure 4 shows the experiment results of fault diagnosis and sensor signal reconstruction.The faults of other sensors are simulated in the same way and the results are listed in Table 2 due to the limited space.It can be learned that when a sensor breaks down, there is an obvious difference between the sensor measurement and the estimated value of the SROS-ELM based estimator.Apparently, the estimated value follows the actual value more tightly than the measured value of the senor with fault.Owing to the fault diagnosis and accommodation strategy, the erroneous sensor signal is abandoned and replaced by the estimated value.Besides, the final output value deviates from the actual value very slightly, which ensures the approximate correctness of the sensor signals provided to the engine controller.Therefore, the engine controller can output right commands according the control law, thereby enabling the engine work properly even in the case of sensor fault.Moreover, from the estimation times in Table 2, it can be seen that all the estimation times are within 1 millisecond and far less than the engine control time step 20 milliseconds, which completely meets the requirements of engine control system for real-time performance.
In the second experiment, fault detection and signal reconstruction for sensors during dynamic process using analytical redundancy technique are validated.The results for   sensor fault are presented in Figure 5, and Table 3 tabulates the results for other sensor faults during dynamic process.It is clear that when a sensor fault occurs, the outputs of the analytical redundancy unit follow the actual values rather than the wrong sensor measurements, which shows that the sensor fault is detected and indicated once the malfunction arises.From Table 3, it can be seen that the sensor measurement estimations have good accuracy, with the maximum relative deviations being about 0.53%.All in all, it shows that the designed analytical redundancy based on SROS-ELM is feasible and effective, thus the operational safety and engine reliability can be enhanced with this technique.

Conclusion
OS-ELM can learn data one-by-one or block-by-block online with fast training speed, but it is quite likely to suffer from singularity or ill-posedness problems.On the basis of OS-ELM, a modified algorithm, SROS-ELM, is proposed in this paper.It selectively updates output weights of neural networks according to the prediction accuracy and the norm of output weight vector, tackles the problems of singularity and ill-posedness by regularization, and adopts a dual activation function in the hidden neurons combing neural networks and wavelet theory to enhance prediction capability.Experiments on the benchmark data sets show that SROS-ELM outperforms some other popular sequential learning algorithms in generalization performance.On the basis of that, a SROS-ELM based aeroengine analytical redundancy technique is developed for sensor faults detection, isolation, and signal reconstruction.Furthermore, the developed technique is verified through HIL simulation on an experimental platform.The experiment results show the effectiveness and feasibility of the SROS-ELM based analytical redundancy technique, which suggests that the technique is a promising approach to improving sensor reliability in aeroengine system.

Fault
Sensor sorting: the ith sensor is removed for y to create vector y

Figure 2 :
Figure 2: Framework of the HIL simulation system.

Figure 2
gives the framework of the HIL simulation system.The actual aeroengine is emulated by a component level model (CLM) with high accuracy running on model computer, which outputs the calculated parameters based on the control inputs from EEC and flight environment such as flight altitude and Mach number.The simulator plays the role of bridging the engine model and EEC by converting the EEC control signals to digital value for engine model calculating and simulating the sensor signals for EEC sampling according to engine model output.

Figure 3 :
Figure 3: Fuel subsystem in the HIL simulation system.

Figure 5 :
Figure 5: Fault diagnostic and signal reconstruction for   sensor during dynamic process.

Table 1 :
Performance comparison on regression application.

Table 2 :
Fault diagnostic and signal reconstruction for  45 sensor under steady state.Experiment results of sensor measurements estimation under steady state.

Table 3 :
Experiment results of sensor measurements estimation during dynamic process.